论文标题
对于矩形网格上的四阶椭圆奇异扰动问题，最低度鲁棒元件方案
Lowest-degree robust finite element scheme for a fourth-order elliptic singular perturbation problem on rectangular grids
论文作者
论文摘要
在本文中，提出了针对四阶椭圆形单数扰动问题的矩形网格上的分段二次不合格元素方法。相对于扰动参数，该提出的方法是牢固收敛的。提出数值结果以验证理论发现。 新方法使用分段二次多项式，可能是最低程度的。有限元空间的最佳顺序近似属性通过新建的本地平均插值操作员证明。但是，这个插值不是一个投影。实际上，我们建立了一个一般理论，并表明没有与本地支持的基础功能相关的本地定义的插值可以投影使用有限的元素空间。特别是，一般理论可以回答[Demko，J。oft。理论，$ \ bf {43} $（2）：151--156，1985]。
In this paper, a piecewise quadratic nonconforming finite element method on rectangular grids for a fourth-order elliptic singular perturbation problem is presented. This proposed method is robustly convergent with respect to the perturbation parameter. Numerical results are presented to verify the theoretical findings. The new method uses piecewise quadratic polynomials, and is of the lowest degree possible. Optimal order approximation property of the finite element space is proved by means of a locally-averaged interpolation operator newly constructed. This interpolator, however, is not a projection. Indeed, we establish a general theory and show that no locally defined interpolation associated with the locally supported basis functions can be projective for the finite element space in use. Particularly, the general theory gives an answer to a long-standing open problem presented in [Demko, J. Approx. Theory, $\bf{43}$(2):151--156, 1985].
